Chemistry 2720, Fall 1996, Test 2 Solutions

Part 1

1. The vapour pressure is related to the equilibrium constant for the process by . For this process,

   

   at 298K. The equilibrium constant at this temperature is

   

   We want the equilibrium constant at 323K. To calculate this, we need :

   

   The vapour pressure of sodium at is therefore .

2. The osmotic pressure is

   

   Thus

   

   or . The number of moles of the protein is therefore

   

   and the molar mass is

   

   Molar masses of this magnitude are usually expressed as 193kg/mol.

3. The overall transport process is

   

   Note that is unaffected because the standard free energies of formation of the glucoses cancel out. The maximum ratio of glucose in to glucose out is obtained when all of the available free energy is begin used up by transport, i.e. when . This implies that

   

   In terms of the activities,

   

   The glucose concentration in the cell can be as high as 71mol/L.

4. The equilibrium is

   

   Let s be the molar solubility. Then

    

   To use the Debye-Hückel equation, we need to express the ionic strength in terms of s.

   

   The Debye-Hückel equation becomes

    

   Use as an initial guess (i.e. assume ideal behaviour) to kick off chain iteration of equations 1 and 2.

   

   The solubility of lead (II) iodide is .

Part 2

1. The key to this kind of problem is to be methodical:

   

2. We expand near x=0.

   

3. If the reaction is endothermic, increasing the temperature should favour products. Conversely, we should decrease the temperature if the reaction is exothermic.

   Since the reaction converts two moles of gas to one, Le Chatelier's principle suggests that increasing the pressure on the system should favour the products.

   We can use free energy coupling to increase the yield if we arrange for one of the reactants to be produced by a reaction with a large, negative .